BIT Numerical Mathematics

, Volume 7, Issue 1, pp 65–70 | Cite as

A note on unconditionally stable linear multistep methods

  • Olof B. Widlund
Article

Abstract

It has been shown by Dahlquist [3] that the trapezoidal formula has the smallest truncation error among all linear multistep methods with a certain stability property. It is the purpose of this note to show that a slightly different stability requirement permits methods of higher accuracy.

Key words

Differential equations multistep methods stability 

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References

  1. 1.
    Dahlquist, G.,Convergence and stability in the numerical integration of ordinary differential equations, Math. Scand. 4 (1956), 33–53, MR 18 338.Google Scholar
  2. 2.
    Dahlquist, G.,Stability and error bounds in numerical integration of ordinary differential equations, Transactions of the Royal Institute of Technology, Stockholm, No. 130, 1959, MR 21 1706.Google Scholar
  3. 3.
    Dahlquist, G.,A special stability problem for linear multistep methods, BIT 3 (1963), 27–43, MR 30 715.Google Scholar
  4. 4.
    Henrici, P.,Discrete variable methods in ordinary differential equations, John Wiley & Sons, Inc., New York, London, 1962, MR 24 B 1772.Google Scholar
  5. 5.
    Henrici, P.,Error propagation for difference methods, John Wiley & Sons, Inc., New York, London, 1963, MR 27 4365.Google Scholar
  6. 6.
    Marden, M.,The geometry of the zeros of a polynomial in a complex variable, Mathematical Surveys No. 3, American Mathematical Society, New York, 1949, MR 11 101.Google Scholar

Copyright information

© BIT Foundations 1967

Authors and Affiliations

  • Olof B. Widlund
    • 1
  1. 1.Department of Computer SciencesUniversity of UppsalaUppsalaSweden

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